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Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ. Prove: ΔWXY ~ ΔWVZ Triangle W X Y is shown. Line segment Z V is drawn parallel to side Y X to form triangle W V Z. Complete the steps of the proof. ♣: ♦: ♠:

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Answer:

The answer is below

Step-by-step explanation:

Two triangles are similar if the ratio of their corresponding sides are in the same proportion.

1. ΔWXY is isosceles with legs WX and WY      (given)

2. ΔWVZ is isosceles with legs WV and WZ     (given)

3. WX =  WY, WV = WZ  (definition of an isosceles triangle)

4. [tex]\frac{WX}{WY}=1\\\\[/tex]

[tex]\frac{WX}{WY}=\frac{WZ}{WZ} \ \ \[/tex] (definition of ≅)

5. (WZ)(WX) = (WY)(WZ)       (multiplication property)

6. (WZ)(WX) = (WY)(WV)  (substitution property).

7. [tex]\frac{WY}{WZ}=\frac{WX}{WV}[/tex]      (property of proportion)

8. ∠W = ∠W (reflexive property)

9. ΔWXY ~ ΔWVZ (side - angle - side similarity postulate)

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Answer:

♣:  

✔ WX = WY; WV = WZ

♦:  

✔ substitution property

♠:  

✔ SAS similarity theorem

Step-by-step explanation:

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